### The Volokh Conspiracy

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# Does Trump Have a 5% Chance of Winning California?

Prediction markets are generally an effective tool for aggregating opinions about the probability of various events, and I have argued that the legal system should rely on prediction markets for making probabilistic estimates. Usually, I am inclined to give more weight to prediction market estimates than to my own idiosyncratic views. I have no special information on the Presidential election, and so I assume that the prediction market estimate that Trump has a 40% chance of winning the Presidency and a 27% chance on winning the popular vote are about right. After all, if I believed that these predictions were worse the ones I could make independently, I would have much less reason to believe that prediction market forecasts are better than those that government officials can make independently. And these numbers are not all that far off from the best independent forecasts.

And yet, there are times when I must confess to puzzlement in prediction market forecasts, especially near the ends of the probability spectrum. Case in point: PredictIt currently gives the Republican Party greater than a 5% chance of winning California in the 2020 Presidential election. Roughly *twice as many *voters in California say that they will vote for Biden than for Trump. My own independent estimate of Trump's chances in California: 0%. The best story that I can make for the Republicans winning the state involves Trump dropping out, Biden turning out to have Alzheimer's disease (but refusing to quit), and hugely disproportionate turnout as a result of the coronavirus. Each of these strikes me as unlikely, and the joint probability that these would also occur *and *be enough for the Republicans to win California strikes me as no greater than 1%. I suppose one could imagine that North Korea or Russia might threaten to drop a nuclear bomb on California if Biden wins, but the probability of that seems extremely small.

Maybe bettors really do think that Trump will be able to cheat. But it seems absurd to me to assign more than a trivial probability to the prospect that he could cheat and get away with it in a state dominated by Democratic officeholders. Sure, maybe Postal Service shenanigans might affect some voters, but it's hard to see it affecting one party much more than the other or being anywhere near the size needed to change the result in California.

Part of the answer, I think, is that PredictIt charges fees, including a 5% fee to process withdrawals. So, if you don't have money invested in PredictIt, you can't make money by investing with PredictIt and betting on the Democrats to win California. My suspicion is that if PredictIt did not have fees (or even better, used a subsidized market maker), the Democrats' odds in California would be higher. Still, that may not be a complete explanation. There are people who have money invested in PredictIt who are willing to pay around 5 cents of their captive cash for a share that will be worth $1 only if the Republicans win California. Meanwhile, it is not infrequent for a low-probability event to be priced on PredictIt as 1%. Moreover, Predictit thinks that the Democrats have around a 98% chance of winning DC, and so market participants seem to believe that the increased support for Trump and Republicans in California relative to DC makes a substantial difference in the likelihood of victory. (This suggests, incidentally, that relatively little of the California prediction can be accounted for by the probability of cheating.)

My best theory is that there may be some manipulation in the market — that is trading at least partly for the purpose of generating excitement in the prospect that the Republicans might win California. If there were no fees on PredictIt, then such manipulation would create profit opportunities for third parties, who would take as many bets at these odds as they could, until the manipulator ran out of funds. But with fees, arbitrage may not be profitable, and so a little bit of manipulation can go a long way on a relatively thinly traded market, or at least can buy a couple of percentage points cheaply. It especially may not be all that profitable for market participants to spend a lot of time thinking about whether the price level reflects fundamentals. Even in a market without fees, manipulation can be at least somewhat successful if others assign some positive probability estimate to the possibility that the manipulators are actually trading based on fundamentals. Of course, if there is manipulation on the California market, there may well be some manipulation in the same direction on the main market, so maybe one should mentally shave one or two points off the estimate of the GOP chances of holding the Presidency.

Whether California has a 0%, 1%, or 5% chance of supporting the Republicans may well matter to whether and how some people vote. If there is a non-negligible chance that California will vote Republican, maybe there is also a non-negligible chance that California will be the tipping point state. There may be a stronger argument for voting third party in a state where the outcome is certain, and maybe there also is a stronger argument for not voting at all. At least some of the incentive to vote may come from the very small probability that one might be the tipping point voter in the entire election, and so it may matter to a voter whether this probability is strictly zero or 1 in a billion.

Still, absent dramatic developments between now and Election Day, I would estimate the probability of Trump winning California at strictly zero. But if the prediction market stays a few percentage points away from that, I must be wrong either about the California voters or in my general view that prediction markets will be relatively accurate even with fees.

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